# A triangle has sides A, B, and C. The angle between sides A and B is pi/6 and the angle between sides B and C is pi/12. If side B has a length of 12, what is the area of the triangle?

Feb 28, 2016

Angle C is $\frac{\pi}{6}$ and angle A is $\frac{\pi}{12}$. Hence angle B= $\pi - \frac{\pi}{6} - \frac{\pi}{12} = \frac{3 \pi}{4}$

Side b =12 , therefore using the formula $\sin \frac{A}{a} = S \in \frac{B}{b}$

it would be side a= b sinA/ SinB= $12 \sin \frac{\frac{\pi}{12}}{\sin} \left(\frac{3 \pi}{4}\right)$

For area of triangle use the formula $\frac{1}{2} a b \sin C$

=$\left(\frac{1}{2}\right) 12 \left(12\right) \sin \frac{\frac{\pi}{12}}{\sin} \left(\frac{3 \pi}{4}\right) \sin \left(\frac{\pi}{6}\right)$

= $72 \left(0.2588\right) \frac{0.5}{0.7071}$

=13.176